when 5 radical 20 is written in simplest form, the result is k radical 5 what is the value of k?
1) 20
2) 10
3) 7
4) 4
10
10
To simplify 5√20, we need to find the largest perfect square that divides 20. The largest perfect square that divides 20 is 4, which is equal to 2^2.
Next, we divide 20 by 4, which gives us 5.
So, 5√20 is equal to 5(2√5).
Therefore, the value of k is 2.
The correct answer is 4) 2.
To simplify the expression 5√20, we need to simplify the radical by breaking down the number inside the radical into its prime factors.
The prime factorization of 20 is 2 x 2 x 5. We can then rewrite the expression as 5√(2 x 2 x 5).
Taking out any pairs of numbers from inside the radical, we can simplify it as shown:
5√(2 x 2 x 5) = 5√(2^2 x 5)
= 5 x 2√5
= 10√5
Therefore, when 5√20 is written in simplest form, it is equal to 10√5.
From the given options, k represents the coefficient of the simplified radical, which in this case is 10. Therefore, the value of k is 10.
So, the correct answer is option 2) 10.